Question

Circle E has a radius of 5.3 meters. FG is a chord and HE is a perpendicular bisector of FG If FG = 6.8 meters, calculate the distance of IH.

Answer 1

Step 1: Given data:

EI = 5.3m radius

EF = 5.3m radius

HF = FG/2 = 6.8/2 = 3.4m

Step 2: Method

`\begin{gathered} \text{Use pythagoras theorem to find the value of EH} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ \text{Opposite = }3.4\text{ m} \\ \text{Adjacent = EH} \\ \text{Hypotenuse = 5.3} \\ 3.4^2+EH^2=5.3^2 \\ 11.56+EH^2\text{ = 28.09} \\ EH^2\text{ = 28.09 - 11.56} \\ EH^2\text{ = 16.53} \\ EH\text{ = }\sqrt[]{16.53} \\ EH\text{ = 4.06} \end{gathered}`

Step 3: Final answer

EI = EH + IH

5.3 = 4.06 + IH

IH = 5.3 - 4.06

IH = 1.24 m